Recalling the discrete choice formulation of the matching problem in (3.5), it is easy to see how changes in preferences lead to variation in optimal matching patterns, and gener- ate relevant general equilibrium effects.
Proposition 1. For βiN ≥ 0 βNj ≥ 0, ui and vj are not decreasing function in βiN and βNj,
respectively.
Proof. Consider the expected maximization problem of man m with trait i, before he knows his realization of em
ij. ui is an increasing and convex function, corresponding to the
expectation of the maximum of linear functions. By the envelope theorem, the effect on uiof
a marginal increase in the systematic component is equivalent to the conditional probability
µj|i, i.e. the probability for man m of choosing j conditional on being of type i. Given:
ui = E max j∈J0 {αij+τij+βiN1{i6=N, j= N} +emij} ∂ui ∂βI N = Pr " αij+τij+βiN1{i6=N, j= N} +eijm ≥ αik+τik+βik1{i6= N, k= N} +emik, ∀k 6=j∈ J0 # ,
16 Galichon and Salani´e(2015) reach the same result and provide a generalization of theChoo and Siow (2006b)’s model applying convex analysis results to discrete-choice models. Maintaining the separability and large market assumptions, they provide an equilibrium characterization of the matching patterns as function of model primitives and derive identification of the joint surplus, in a more general distributional setting.
where µj|i = Pr " αij+τij+βiN1{i6= N, j= N} +emij ≥ αik+τik+βik1{i6=N, k= N} +eikm, ∀k6= j∈ J0 # .
Under the assumption that the legal status acquisition increases the value of an intereth- nic marriage, i.e. βiN ≥ 0 βNj ≥ 0, granting the legal status to new EU member migrants
independently from marital reasons, the EU enlargements induced a negative variation in gains to intermarriage. Thus, I expect to observe a reduction in the number of intermar- riages with migrants from new EU member countries, in response to the exogenous change. Moreover, I expect the response to the legal status acquisition to be highly heterogeneous across migrants’ ethnicities, with the magnitude of the negative effect to be inversely pro- portional to the socio-economic conditions of immigrants before the intervention.
3.5
The Data
I estimate gains to marriage along cultural lines from equation (3.6), using administra- tive Italian data on marriages (1997-2012) and individual Census data on population vectors (1991, 2001, 2011). I describe below the data used in the empirical analysis.
Marriages (1998-2012). I recover matching patterns by spouses’ ethnic identity (µij ∀i∈
I,∀j ∈ J), exploiting marriage records from municipality vital statistics registries. Vital statistics registries contain the universe of marriages celebrated each year in Italy from 1997 to 2012. Marriage records provide information about the date of marriage, the celebration ceremony (religious or civil), the municipality of celebration and the choice of the property regime by the spouses (community or separation property). The information provided for each spouse include: the date of birth, the municipality of birth, the municipality of resi- dence at the time of marriage, the province of future residence of the spouses, the previous marital status, the education level, the employment status, and for migrant individuals the nationality and the country of origin17.
Individual Census Data (1991, 2001, 2011). Population vectors of unmatched individuals by gender and by ethnic identity (µi0, µ0j) come from individual Italian Census data for the
years 1991, 2001, 2011. I select only adult individuals, of more than 18 years of age. Census data classify the marital status of an individual as: never married, at present married, sep- arated de facto, legally separated, divorced or widowed. I consider an individual available
17In 1997 only the nationality of foreign-born individuals is provided, because the information of the country
of birth was not collected. Despite the naturalization process was not frequent at the time, the nationality might underestimate the number of migrant individuals. To overcome the measurement error issue, I report estimates exploiting both a two-year marriage distribution for the period from 1997 to 2012, and a one-year distribution for the period from 1998 to 2012.
in case she/he is never married, legally separated, divorced or widowed.
For the sake of the empirical application, two features require to be highlighted. First, differences in cultural traits are evaluated with respect to the ethnic identity of spouses, proxied by the country of origin. I restrict the set of spouses’ ethnicities to a finite number of political-ethnic groups, to have thicker cells of the marital distribution. The classifica- tion of countries reflects both the cultural-ethnic proximity of each country with respect to Italy, and its economic and socio-political proximity. The list of countries belonging to each political-ethnic group is reported in TableC.1. In particular, I divide the former EU member countries between Northern European countries, EU15German, and Southern Eu- ropean countries, EU15Latin. Countries that became part of the EU in 2004 are denoted by EU10, while those that entered the EU in 2007 are denoted by EU2. FollowingMastrobuoni and Pinotti (2015), among the remaining East European countries, I differentiate between those countries that were negotiating admission conditions with the EU at the time of my analysis, EUNext, and all the remaining ones, EUOther. Finally, I split all other countries into North Africa, A f ricaN; South-West and East Africa, A f ricaWES; South-West Asia, AsiaWS; East Asia and Oceania islands, AsiaE; and the rest of developed OECD countries, OECD. In the rest of the empirical discussion, I focus my attention on the analysis of het- erogamous wife intermarriages, which largely dominate the overall number of intermarriages formed in Italy18. Secondly, compared to the theoretical model, I enlarge the type space of
individuals, considering a multi-market framework. I exploit both time variability and ge- ographical variability across Italian provinces. I investigate both a one-year and a two-year marital distribution. Estimates from a two-year distribution, are reported as robustness, because it returns thicker cells. Moreover, I consider multiple local marriage markets at the province level. Let t ∈ T denote the time dimension, while p ∈ P refers to provinces. For instance, each match is now characterized by the ethnic identities of the spouses i and j, by the time-year of the marital union t, and the province of residence of spouses p at the moment of the marriage. Thus, gains to marriage φij,tp belong to the space I×J×T×P.
I estimate gains to marriage along ethnic lines, from equation (3.6), for each i, j match, for each time-year t and for each province p, as follow:
ˆ
φij,tp =ln
µij,tp
√
µi0,tpµ0j,tp. (3.7)
To estimate marital gains, I approximate the evolution of population vectors over time as follows. First, I calculate the difference in the number of unmatched individuals by gender and by ethnicity from 1991 to 2001 and from 2001 to 2011. Similarly, I consider the increase in migration patterns by ethnicity and I calculate the difference in the number of
foreign individuals from 1995 to 2010 and I compute for each year the corresponding share. Finally, I impute to each year a share of the overall difference of unmatched individuals, that is proportional to the migration variation share. The imputation allows to take into account the fact that different ethnicities experience heterogeneous rates of migration over time.
I recover the evolution of the number of marriages formed in Italy over time, as well as the number of available foreign individuals and the estimated gains to intermarriage, for each political-ethnic group. The time variation in the total number of marriages across the political-ethnic groups differs in magnitude. Intermarriages between Italian men and foreign women from new EU member countries highly decrease, whereas intermarriages between Italian men and foreign women from other countries decrease, but at lower rate. Conversely, the Figure evidences a disproportionate increase of available foreign women from new EU member countries, especially for EU2 women, as opposed to women be- longing to the other groups. It is this differential in pre-post EU enlargements variation of marriage patterns across political-ethnic groups and the pre-post variation in population vectors that provide identification of the fall in gains to intermarriage, in response to the legal status acquisition.